Dynamic Aperture Studies Research Articles

Optimizing dynamic aperture studies with active learning

Dynamic aperture is an important concept for the study of non-linear beam dynamics in circular accelerators. It describes the extent of the phase-space region where a particle's motion remains bounded over a given number of turns. Understanding the features of dynamic aperture is crucial for the design and operation of such accelerators, as it provides insights into nonlinear effects and the possibility of optimising beam lifetime. The standard approach to calculate the dynamic aperture requires numerical simulations of several initial conditions densely distributed in phase space for a sufficient number of turns to probe the time scale corresponding to machine operations. This process is very computationally intensive and practically outside the range of today's computers. In our study, we introduced a novel method to estimate dynamic aperture rapidly and accurately by utilising a Deep Neural Network model. This model was trained with simulated tracking data from the CERN Large Hadron Collider and takes into account variations in accelerator parameters such as betatron tune, chromaticity, and the strength of the Landau octupoles. To enhance its performance, we integrate the model into an innovative Active Learning framework. This framework not only enables retraining and updating of the computed model, but also facilitates efficient data generation through smart sampling. Since chaotic motion cannot be predicted, traditional tracking simulations are incorporated into the Active Learning framework to deal with the chaotic nature of some initial conditions. The results demonstrate that the use of the Active Learning framework allows faster scanning of the configuration parameters without compromising the accuracy of the dynamic aperture estimates.

Dynamic aperture studies for vertical fixed field accelerators

Vertical orbit excursion Fixed Field Accelerators (vFFAs) feature highly nonlinear magnetic fields and strong transverse motion coupling. The detailed study of their Dynamic Aperture (DA) requires computation codes allowing long-term tracking and advanced analysis tools to take the transverse motion linear and nonlinear coupling into account. This coupling completely transforms the beam dynamics compared to a linear uncoupled motion, and an explicit definition of the DA is needed to characterize the performance and limitations of these lattices. A complete study of the DA in the 4D phase space in highly nonlinear and strongly coupled machines must give a measure of the stability domain but also means to assess the operating performance in the physical coupled space. This work presents a complete set of methods to perform such detailed analysis. These methods were explored and compared to compute and characterize the DA of an example vFFA lattice. The whole procedure can be further applied to evaluate DA using realistic models of the magnetic fields, including fringe fields and errors.

A Framework for Dynamic Aperture Studies for Colliding Beams in the High-Luminosity Large Hadron Collider

A Framework for Dynamic Aperture Studies for Colliding Beams in the High-Luminosity Large Hadron Collider

Frequency analysis and dynamic aperture studies in a low energy antiproton ring with realistic 3D magnetic fields

We briefly present recent progress with our algorithm and its implementation called SIMPA described in a previous paper. The algorithm has a new and unique approach to long-term 4D tracking of charged particles in arbitrary static electromagnetic fields. Using the improvements described in this paper, we made frequency analysis and dynamic aperture studies in ELENA. The effect of the end fields and the perturbation introduced by the magnetic system of the electron cooler on dynamic aperture is shown. A special feature of this study is that we have not introduced any multipole errors into the model. The dynamic aperture calculated in this paper is the direct consequence of the geometry of the magnetic elements. Based on the results, we make a few suggestions to reduce the losses during the deceleration of the beam.

SPPC/CEPC lattice design and beam dynamics study

In this paper, we introduced the parameter choice and the first version lattice design for a 61 km and 100-km Super Proton–Proton Collider (SPPC). We started the lattice design and the beam dynamics study from last year and showed the preliminary dynamic aperture result of these two SPPC lattice versions. We also showed the layout, the lattice design and the dynamic aperture study of a CEPC partial double ring, an advanced partial double ring and a fully partial double ring schemes.

CEPC partial double ring lattice design and SPPC lattice design

In this paper, we introduce the layout and lattice design of Circular-Electron-Positron-Collider (CEPC) partial double ring scheme and the lattice design of Super-Proton-Proton-Collider (SPPC). The baseline design of CEPC is a single beam-pipe electron positron collider, which has to adopt pretzel orbit scheme and it is not suitable to serve as a high luminosity [Formula: see text] factory. If we choose partial double ring scheme, we can get a higher luminosity with lower power and be suitable to serve as a high luminosity [Formula: see text] factory. In this paper, we discuss the details of CEPC partial double ring lattice design and show the dynamic aperture study and optimization. We also show the first version of SPPC lattice although it needs lots of work to do and to be optimized.

Numerical study of dynamic fracture aperture during production of pressure-sensitive reservoirs

In fractured reservoirs, some dynamic behavior, such as fracture opening or closure and fracture shear dilation, is induced by the variation of pressure and in-situ stress, which is associated with the fracture aperture and conductivity. In this paper, we focus on the dynamic behavior of fractures and various kinds of affecting factors, including in-situ stress, lithology and fluid pressure. A mathematical model for numerical simulation of the fracture dynamic behavior is developed, which consists of a matrix-fracture stress–strain model and a matrix-fracture flow model. The stress–strain model of fractures is derived, which contains two sections of shear dilation: before-peak dilation and after-peak shear dilation. Then a discrete fracture network (DFN) technology is used to depict the shape of fractures in reality and the model is solved by the finite element method to investigate what the range-ability the fracture aperture presents under the influence of the affecting factors. Based on this model, the effects of pressure distribution, lithology, anisotropic in-situ stress and well production proration are investigated and the specific effects by different affecting factors are analyzed. The numerical outcome indicates that the fracture aperture increases as the field pressure rises. The anisotropic in-situ stress and water injection can trigger large shear dilation, which serves as a positive function in fracture opening.

ILC 3.2 km damping ring design based on the FODO cell

We report on a new design for an ILC 3.2 km damping ring, with 2 arcs based on the FODO cell and 2 straight sections that are nearly the same as the newest version of the 6.4 km ring DCO4. This new lattice requires fewer magnets and a lower RF voltage, and has a better dynamic aperture than DCO4 while maintaining flexibility in regard to the momentum compaction factor. So far, this design is the only one satisfying all the requirements for a 3.2 km ring. The work on the lattice design and the dynamic aperture study is presented in detail.

Nonlinear correction schemes for the phase 1 LHC insertion region upgrade and dynamic aperture studies

The phase 1 LHC interaction region (IR) upgrade aims at increasing the machine luminosity essentially by reducing the beam size at the interaction point. This requires a total redesign of the full IR. A large set of options has been proposed with conceptually different designs. This paper reports on a general approach for the compensation of the multipolar errors of the IR magnets in the design phase. The goal is to use the same correction approach for the different designs. The correction algorithm is based on the minimization of the differences between the IR transfer map with errors and the design IR transfer map. Its performance is tested using the dynamic aperture as a figure of merit. The relation between map coefficients and resonance terms is also given as a way to target particular resonances by selecting the right map coefficients. The dynamic aperture is studied versus magnet aperture using recently established relations between magnetic errors and magnet aperture.

Quadruple-bend achromatic low emittance lattice studies

A quadruple-bend achromatic (QBA) cell, defined as a supercell made of two double-bend cells with different outer and inner dipole bend angles, is found to provide a factor of 2 in lowering the beam emittance relative to the more conventional double-bend achromat. The ratio of bending angles of the inner dipoles to that of the outer dipoles is numerically found to be about 1.5-1.6 for an optimal low beam emittance in the isomagnetic condition. The QBA lattice provides an advantage over the double-bend achromat or the double-bend nonachromat in performance by providing a small natural beam emittance and some zero-dispersion straight sections. A lattice with 12 QBA cells and a preliminary dynamic aperture study serves as an example.

Dynamic aperture study for the Duke FEL storage ring

The new lattice design of the Duke free electron laser (FEL) storage ring is described. The results of the 6-dimensional dynamic aperture study using single particle tracking codes are presented. The influence of 8-m FEL undulator on the dynamic aperture is studied.